Trusses were the most popular bridges for a century and a half. Built from timber, iron, and eventually steel, the lightweight and long-spanning forms also had the advantage of providing a flat deck for railroads and later highways. They have fallen out of favour recently, although long-span arches may still show a secondary truss structure, like the New River Gorge Bridge in West Virginia.
In a freshman-level structural mechanics class, budding engineers learn about many types of trusses, but they rarely learn the advantages and disadvantages of each type. I’d like to rectify that in my little way.
A Howe truss has diagonals that slope up toward the middle of the bridge. Verticals are in tension; diagonals are in compression. Howe trusses are rare because compression is more expensive than tension – that is, a steel or wood member of a given size is stronger in tension. More common is a Pratt truss, which has diagonals that slope down toward the middle of the bridge. Verticals are in compression; diagonals are in tension. Another variation is a Brown truss which has X-shaped diagonals; one leg of each X is always in tension. Brown trusses are common in older wood and iron bridges, using metal rods for diagonals.
A Warren truss has diagonals that alternate sloping up and down and no verticals at all. Because of the efficient shape of equilateral triangles, they tend to use a minimum of material. A Vierendeel truss, conversely, has no diagonals. Vierendeels are not true trusses because the verticals work in flexure (bending), not pure tension and compression. As a result the verticals tend to be very beefy.
Some engineers have designed trusses like the K-truss where the diagonals try to mimic the curved paths that loads take in a beam. The result is lightweight but expensive because of the extra connections.